Bangalore, led by the talismanic India skipper, needed a six off the last delivery to tie the match against Mumbai but batsman Shivam Dube could only hit Lasith Malinga's full-length delivery to long-on to lose by six runs.
Replays showed the Sri Lanka fast bowler had clearly overstepped the crease for a no-ball, meaning a free hit for Bangalore.
"We are playing at IPL level, not club cricket," a livid Kohli said at the post-match presentation. "That's just a ridiculous call off the last ball. The umpires should have their eyes open, it was a no-ball by an inch.
"It's a completely different game altogether (with the extra delivery). So if it's a game of margins, I don't know what's happening. They should have been more sharp and more careful out there."
The no-ball would have resulted in an extra run for Bangalore and brought former South Africa batsman AB de Villiers on strike. De Villers was in scintillating form and unbeaten on 70 off 41 balls with half a dozen sixes and four fours.
Thursday's loss was the second in as many matches for the Kohli-led side while Mumbai picked up their first victory.
Mumbai skipper Rohit Sharma, who is Kohli's deputy in India's limited-overs sides, was also unimpressed with the umpiring gaffe.
"These kinds of mistakes are not good for the game of cricket," Sharma said. "The players can't do much about it... but I hope they can rectify their mistakes like we do.
"It's pretty simple, those decisions can cost you games. We prepare too much to win this tournament, to win games, and those kind of mistakes are not acceptable."
The controversy comes days after Ravichandran Ashwin's 'Mankad' dismissal of Jos Buttler in a match between Rajasthan and Punjab caused uproar.
The tournament, however, is in rude health in terms of viewership, with the 12th edition set to surpass all previous records. Broadcasters Star India said viewership for the opening weekend rose 31 percent to 219 million from the previous year.
(Reporting by Sudipto Ganguly; editing by Ian Ransom)
